Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 7. f(x) = sin(x) F(x)=

Question

Find an antiderivative F(x) with F '(x) = f(x) and F(0) = 7.

f(x) = sin(x)

F(x)=

Answer 1

f(x) = sin(x)

 

F(x) = -cos(x) + c

 

F(0) = 7

 

7 = -cos(0) + c = -1 + c ⇒ c = 8

 

F(x) = -cos(x) + 8